For a little historical perspective, which at least explains why older books on non-elementary mathematics rarely have "solutions":
Imagine first that there's no internet, that long-distance phone calls are prohibitively expensive, and that photocopying is not only expensive but mostly inaccessible to students. Imagine also that people use the same homework and exam questions over-and-over. The only step needed to prevent gaming the system is to not put solutions in the book (or in the library, either). Done.
In combination with that immobility of information, there was a sort of macho culture of not telling anyone who couldn't already do a problem how to do it. This is perverse from an educational or scientific viewpoint, of course, but that doesn't mean that humans won't do it. That is, homeworks and exams would be graded, and points subtracted, and things marked "nonsense", without any "approved solution" being given, much less "published".
The common student complaint that they can't tell whether their own "solution/proof/computation" is correct... raises a different point, namely, that students should be very strongly encouraged to develop exactly the sensibilities to know at least roughly whether they're doing the right thing. (The culture of math as rules imposed by an ineffable external authority doesn't help.)
Ignoring that misguided complaint, my complaint is that there are many important, useful, traditional questions/issues with essentially no expert-written treatments... because they're always assigned as exercises... but/and crappy very-inexpert solutions or pseudo-solutions or non-solutions do circulate, thus misleading, certainly not helping, myriad yet-more-junior students.
Thus, by now, given the mobility of information, I think good, that is, "expert", solutions should be available. Yes, this does entail that "assessment" methods have to change. So be it. Also, people can read and write.